منابع مشابه
κ-Complete Uniquely Complemented Lattices
We show that for any infinite cardinal κ , every complete lattice where each element has at most one complement can be regularly embedded into a uniquely complemented κ-complete lattice. This regular embedding preserves all joins and meets, in particular it preserves the bounds of the original lattice. As a corollary, we obtain that every lattice where each element has at most one complement ca...
متن کاملThe Macneille Completion of a Uniquely Complemented Lattice
Problem 36 of the third edition of Birkhoo's Lattice theory 2] asks whether the MacNeille completion of uniquely complemented lattice is necessarily uniquely complemented. We show that the MacNeille completion of a uniquely complemented lattice need not be complemented. Questions regarding the axiomatics of Boolean algebras led Huntington to conjecture , in 1904, that every uniquely complemente...
متن کاملOn the Complemented
Rosenthal [R] introduced the Lp space Xp in 1971. Among its interesting properties are that it contains and is contained in isomorphs of lp ⊕ l2, but is not isomorphic to a complemented subspace of lp⊕ l2. These properties have made Xp rather resistant to standard approaches to classifying its complemented subspaces. For example it was first proved that Xp was primary in [JO2] where the device ...
متن کاملCompletely Complemented Subspace Problem
Communicated by Abstract. We will prove that, if every finite dimensional subspace of an infinite dimensional operator space E is 1-completely complemented in it, E is 1-Hilbertian and 1-homogeneous. However, this is not true for finite dimensional operator spaces: we give an example of an n-dimensional operator space E, such that all of its subspaces are 1-completely complemented in E, but whi...
متن کاملOn Contractively Complemented Subspaces
Abstract. It is shown that for an L1-predual space X and a countable linearly independent subset of ext(BX∗) whose norm-closed linear span Y in X∗ is w∗-closed, there exists a w∗-continuous contractive projection from X∗ onto Y . This result combined with those of Pelczynski and Bourgain yields a simple proof of the Lazar-Lindenstrauss theorem that every separable L1-predual with non-separable ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Order
سال: 2017
ISSN: 0167-8094,1572-9273
DOI: 10.1007/s11083-017-9440-5